0610. Two firms in the Waikato region of New Zealand produce the same product in a competitive industry. Each has an old factory using an old technology. It still pays to operate these factories but it would not pay to expand them. The only variable factor used by either firm is labour. Each firm pollutes the other and thus reduces the output of the other firm. The production functions of firms A and B respectively are Qa = L^0.5a - (2/3)Qb and Qb = L^0.5b - (1/3)Qa, where L^0.5a and L^0.5b are the square roots respectively of the amount of labour used by firms A and B. The wage rate of labour is $1 and the price of the firms' output is $12.

a) If the two firms each maximise profits independently, how much output would each firm produce? How much quasi-rents would each factory earn?

b) If someone buys both the firms and maximises joint profits, how much total output would be produced? How much quasi-rent is earned in total?

c) Briefly explain the change in your answer to part (b) from part (a).